The generator matrix

1 0 0 0 0 0 0 1 1 1 1 0 1 1 1 2 0 2 0 1 2 0 1 0 2 1 1 1 2 2 1 2 1 0 0 0 1 1 1 1 0 1 0 1 1 2 2 2 0 0 0 1 1
0 1 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 2 1 1 1 1 1 1 3 1 3 2 1 2 1 1 1 1 2 2 1 1 1 1 0 1 1 0 0 1 0 1 0 1 0 0
0 0 1 0 0 0 0 0 0 0 0 2 1 3 3 1 1 1 1 1 2 0 3 3 1 1 2 2 0 0 1 1 3 1 3 1 2 0 2 2 1 3 0 1 3 2 2 0 2 1 2 0 0
0 0 0 1 0 0 0 1 0 0 3 1 2 3 3 0 3 3 1 3 1 2 1 3 0 2 2 0 1 2 1 2 0 0 1 0 0 3 3 2 0 3 0 1 2 0 1 1 1 0 1 0 0
0 0 0 0 1 0 0 1 2 3 0 3 0 2 3 0 0 3 2 2 3 3 1 2 3 2 2 0 1 1 3 0 3 3 2 3 3 0 1 2 0 2 2 2 0 1 1 2 2 3 3 0 0
0 0 0 0 0 1 0 1 3 2 2 1 3 2 1 1 0 3 1 1 1 1 0 1 1 2 0 3 2 2 0 0 2 2 1 1 3 1 1 2 3 3 1 3 1 3 0 3 1 1 3 0 0
0 0 0 0 0 0 1 2 1 3 1 3 0 0 1 3 3 1 2 3 0 1 3 2 2 1 2 3 1 2 3 0 2 3 1 1 2 2 1 1 3 1 0 2 3 3 1 0 3 2 3 0 0

generates a code of length 53 over Z4 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+96x^40+374x^42+817x^44+1060x^46+1541x^48+1976x^50+2338x^52+2166x^54+2201x^56+1584x^58+1091x^60+624x^62+318x^64+144x^66+41x^68+6x^70+3x^72+2x^74+1x^84

The gray image is a code over GF(2) with n=106, k=14 and d=40.
This code was found by Heurico 1.10 in 10.3 seconds.